Question

Find the measure of each interior angle AND each exterior angles of the following polygons. Show your work.

A.) Pentagon.

B.) 16-gon.

C.) Dodecagon

Answer 1

The sum of all measures of interior angles in a polygon with n sides is given by formula
`(n-2)180^(\circ)`.

The sum of all measures of exterior angles in a polygon with n sides is always
`360^(\circ)`.

Then

A) For a pentagon, n=5.

The sum of all measures of interior angles in a pentagon is
`(5-2)180^(\circ) =540^(\circ)`.

B) For a 16-sided polygon, n=16.

The sum of all measures of interior angles in a 16-sided polygon is
`(16-2)180^(\circ) =2520^(\circ)`.

B) For a dodecagon, n=12.

The sum of all measures of interior angles in a dodecagon is
`(12-2)180^(\circ) =1800^(\circ)`.

If these polygons are regular or equiangular, then

A) Interiror angle has measure
`(540^(\circ))/(5) =108^(\circ)` and exterior angle has measure
`(360^(\circ))/(5) =72^(\circ)`.

B) Interiror angle has measure
`(2520^(\circ))/(16) =157.5^(\circ)` and exterior angle has measure
`(360^(\circ))/(16) =22.5^(\circ)`.

C) Interiror angle has measure
`(1800^(\circ))/(12) =150^(\circ)` and exterior angle has measure
`(360^(\circ))/(12) =30^(\circ)`.